In triangle ABC, angle c is 90 AB = 10 sin A = √ 21/5 find AC.

We find ac in the triangle abc if it is known:

Angle C = 90 °;

ab = 10;

sin a = √21 / 5.

Decision.

1) Find the cosine of the angle a, if the value of the sine of the angle a is known.

We get:

sin ^ 2 a + cos ^ 2 a = 1;

(√21 / 5) ^ 2 + cos ^ 2 a = 1;

21/25 + cos ^ 2 a = 1;

cos ^ 2 a = 1 – 21/25;

cos ^ 2 a = 25/25 – 21/25;

cos ^ 2 a = 4/25;

cos ^ 2 a = (2/5) ^ 2;

cos a = 2/5;

cos a = 0.4;

2) Find the leg ac.

cos a = ac / ab;

From here we express ac and substitute the known values and calculate the leg.

ac = ab * cos a = 10 * 0.4 = 10 * 4/10 = 10/10 * 4 = 1 * 4 = 4;

Answer: ac = 4.